
where \(m_Z\)  and \(m_W\)  are the SM weak gauge boson masses, the cosine of the weak mixing angle \(c_{W}^{2}=m_{W}^{2}/m_{Z}^{2}\)  and \(s_{W}^{2}=1-c_{W}^{2}\) . The loop functions \(f_T(x)\)  and \(f_S(x)\)  are given by [1]}, [2]}
\(f_{T}(x)&=\frac{x \log x}{x-1},\\f_{S}(x)&={\left\lbrace \begin{array}{ll}\displaystyle {\frac{1}{12}\left[-2x^{2}+9x+\left((x-3)\left(x^{2}-4 x+12\right)+\frac{1-x}{x}\right) f_{T}(x)\right.}\\\displaystyle \qquad {\left.+2 \sqrt{(4-x) x}\left(x^{2}-4 x+12\right) \tan ^{-1}\sqrt{\frac{4-x}{x}}\right],~ \mbox{for~} 0<x<4,}\\\displaystyle {\frac{1}{12}\left[-2 x^{2}+9 x+\left((x-3)\left(x^{2}-4x+12\right)+\frac{1-x}{x}\right) f_{T}(x)\right.}\\\displaystyle \qquad {\left.+\sqrt{(x-4) x}\left(x^{2}-4 x+12\right) \log \left(\frac{x-\sqrt{(x-4) x}}{x+\sqrt{(x-4) x}}\right)\right],~ \mbox{for~} x \ge 4.}\end{array}\right.}\) 
